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if S1 , S2 , S3..........,Sq are the sum...

if `S_1 , S_2 , S_3..........,S_q` are the sums of `n` terms of `q ,AP's` whose first terms are `1,2,3,...........q` and common difference are `1,3,5,...........,(2q-1)` respectively ,show that `S_1 + S_2 + S_3..........+S_q=1/2nq(nq+1)`

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. Given an A.P. whose terms are all positive integers. The sum of its fi...

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  2. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  3. if S1 , S2 , S3..........,Sq are the sums of n terms of q ,AP's whose ...

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  4. If S1 be the sum of (2n+1) term of an A.P. and S2 be the sum of its od...

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  5. The number of terms in an AP is even. The sum of the odd terms is 24 w...

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  6. The ratio of the sums of n terms of two Aps is (3n-13) : (5n+21). Find...

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  7. Find the AP in which the ratio of the sum to n terms to the sum of suc...

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  8. If x,2x+2,3x+3 are the first three terms of a GP, find the fifth term ...

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  9. In a GP, t4=27 and t7=729. Find t(11) where tn denotes the nth term.

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  10. In a GP, t4=27 and t7=729. Find t(11) where tn denotes the nth term.

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  11. In a GP, t(p+q)=a and t(p-q)=b. Prove that tp=sqrt(ab).

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  12. If the pth, qth and rth terms of a G.P. are a,b and c, respectively. ...

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  13. If a be the first term, b be the nth term and P be the product of n te...

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  14. If a,b,c are in GP, prove that (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2).

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  15. If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b...

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  16. If a,b,c,d are in GP then prove that a+b,b+c,c+d are in GP.

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  17. If a,b,c,d are in GP then prove that a(b-c)^3=d(a-b)^3.

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  18. If a,b,c,d are in GP then prove that ax^3+bx^2+cx+d has a factor ax^2+...

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  19. Let a1,a2,a3,.....,an be in GP whose common ratio is r. Show that sum(...

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  20. Does there exist a GP containing 27,8 and 12 as threee of its terms ? ...

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